MySQL中字段排序区分大小写吗？ 如何做到先排序完小写，再排序大写

已知MySQL表结构

mysql> desc books;
+-------+------------+------+-----+---------+-------+
| Field | Type       | Null | Key | Default | Extra |
+-------+------------+------+-----+---------+-------+
| name  | varchar(2) | YES  |     | NULL    |       |
+-------+------------+------+-----+---------+-------+
1 row in set (0.00 sec)

已知表中的数据

mysql> select * from books;
+------+
| name |
+------+
| b    |
| a    |
| c    |
| A    |
| B    |
| C    |
+------+
6 rows in set (0.00 sec)

已知对数据内容排序

mysql> select * from books order by name asc;
+------+
| name |
+------+
| a    |
| A    |
| b    |
| B    |
| c    |
| C    |
+------+
6 rows in set (0.00 sec)

排序结果a,A，都排在了前面，我想知道，如何做到排序结果为

a
b
c
A
B
C

或者是

A
B
C
a
b
c